Theorems · Theorem · functional analysis
div_le_egauge_ball
∀ (𝕜 : Type u_1) [inst : NormedField 𝕜] {E : Type u_2} [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
(r : NNReal) (x : E), ‖x‖ₑ / ↑r ≤ egauge 𝕜 (Metric.ball 0 ↑r) x- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ENNReal.ofNNRealstatement · cited by 1,279
- NNReal.toRealstatement · cited by 1,260
- NormedFieldstatement and proof · cited by 1,084
- Metric.ballstatement · cited by 735
- ENorm.enormstatement · cited by 715
- egaugestatement · cited by 75
- Metric.ball_subset_closedBallproof · cited by 46
Cited by4
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleOTVS_iff_isLittleOproof · cited by 7
- le_egauge_ball_oneproof · cited by 3
- Asymptotics.isBigOTVS_iff_isBigOproof · cited by 3
- Asymptotics.Filter.Tendsto.isBigOTVS_oneproof · cited by 1